diff --git a/Modular_arithmetic/doc_tex/Modular_arithmetic/main.tex b/Modular_arithmetic/doc_tex/Modular_arithmetic/main.tex
index 38bd5f984fd..72a1607004d 100644
--- a/Modular_arithmetic/doc_tex/Modular_arithmetic/main.tex
+++ b/Modular_arithmetic/doc_tex/Modular_arithmetic/main.tex
@@ -25,11 +25,12 @@ Since the type is based on double
 arithmetic the prime is restricted to values less than $2^{26}$. 
 The initial value of $p$ is 67111067. 
 
-Please note that the implementation of class \ccc{CGAL::Residue} requires that 
-doubles are rounded to nearest, that is, it indispensable that the 
-rounding mode is set accordingly before performing any arithmetic operations. 
-For instance you may use \ccc{CGAL::Protect_FPU_rounding} with 
-\ccc{CGAL_FE_TONEAREST}. 
+Please note that the implementation of class \ccc{CGAL::Residue} requires a mantissa 
+precision according to the IEEE Standard for Floating-Point Arithmetic (IEEE 754). 
+However, on some processors the traditional FPU uses an extended precision. Hence, it 
+is  indispensable that the proper mantissa length is enforced before performing 
+any arithmetic operations. For instance you may use \ccc{CGAL::Protect_FPU_rounding} with 
+\ccc{CGAL_FE_TONEAREST}, which enforces the required precision as a side effect. 
 
 \begin{ccAdvanced}      
 In case the flag \ccc{CGAL_HAS_THREADS} 
diff --git a/Modular_arithmetic/doc_tex/Modular_arithmetic_ref/Residue.tex b/Modular_arithmetic/doc_tex/Modular_arithmetic_ref/Residue.tex
index b84bf60f206..02dee56c3fd 100644
--- a/Modular_arithmetic/doc_tex/Modular_arithmetic_ref/Residue.tex
+++ b/Modular_arithmetic/doc_tex/Modular_arithmetic_ref/Residue.tex
@@ -17,11 +17,13 @@ old prime and can be reused after restoring the old prime.
 Since the type is based on double 
 arithmetic the prime is restricted to values less than $2^{26}$. 
 The initial value of $p$ is 67111067. 
-Moreover, the implementation of class \ccc{CGAL::Residue} requires that 
-doubles are rounded to nearest, that is, it indispensable that the 
-rounding mode is set accordingly before performing any arithmetic operations. 
-For instance you may use \ccc{CGAL::Protect_FPU_rounding} with 
-\ccc{CGAL_FE_TONEAREST}. 
+
+Please note that the implementation of class \ccc{CGAL::Residue} requires a mantissa 
+precision according to the IEEE Standard for Floating-Point Arithmetic (IEEE 754). 
+However, on some processors the traditional FPU uses an extended precision. Hence, it 
+is  indispensable that the proper mantissa length is enforced before performing 
+any arithmetic operations. For instance you may use \ccc{CGAL::Protect_FPU_rounding} with 
+\ccc{CGAL_FE_TONEAREST}, which enforces the required precision as a side effect. 
 
 In case the flag \ccc{CGAL_HAS_THREADS} 
 is undefined the prime is just stored in a static member